Other councils are converting church halls, day centres and even a former police station into schools.

But the study – published today – revealed that the bulge in primary numbers will soon creep through into secondary education where almost 81,000 new places will be needed by 2019.

In all, one-in-three local authorities will need to create more places, it emerged.

The disclosure comes just days after it emerged that rising numbers of children had failed to secure their first-choice secondary school this year because of mounting competition for places.

Figures compiled by the Telegraph found that at least four-in-10 children in some parts of the capital had been forced to accept second, third or even sixth-choice schools.

But the LGA warned that the squeeze on secondary places would get worse in coming years.

Cllr David Simmonds, chairman of the LGA’s children and young people board, said: “Since the scale of the surge in demand for school places became clear, councils have done everything in their powers to ensure no child is without an education.

“However, as children move through primary school, securing new secondary places will become a significant issue… The challenge for councils is making sure places are delivered on time and in the right places.

“By giving power to create schools back to councils, government could ensure places for children from the ages of four to 18 can be delivered according to local demand, and in line with the local needs of mums and dads and their children.”

It is believed that rising birth rates seen in the early to mid-2000s – combined with an increase in the number of immigrants in some areas – is leading to a big increase in pupil numbers.

The LGA analysed DfE figures and found that almost 130,000 new primary places would be needed by 2017. It is the equivalent of a fifth being added to the average 600,000 annual reception cohort – or just over 500 completely new schools.

By 2019, a total of 80,716 new secondary places will be needed.

In Reading, an extra 2,593 places are needed – equivalent to 34 per cent of its current capacity. The London Borough of Richmond upon Thames needs an extra 2,020 places – equivalent to 25 per cent of its capacity.

The LGA wants councils to be given greater control over the planning of school places. This is a power many have lost since large numbers of secondaries were given academy status – freeing them of local authority control.